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One used-car salesperson receives a commission of $ 200 plus 4 percent

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One used-car salesperson receives a commission of $ 200 plus 4 percent [#permalink]

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New post 13 Dec 2015, 03:53
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One used-car salesperson receives a commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?

A. $ 5,000
B. $ 6,000
C. $ 8,000
D. $ 10,000
E. $ 12,000
[Reveal] Spoiler: OA

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Re: One used-car salesperson receives a commission of $ 200 plus 4 percent [#permalink]

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New post 13 Dec 2015, 12:01
let s1 and s2 be the commission earned by the two salesperson
as per the question,
s1=200+0.04(x-1000) (where x is the sp of the car)
s2=0.06x
also
s1=s2
or,
200+0.04(x-1000)=0.06x
200+0.04x-40=0.06x
0.02x=160
x=8000

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Re: One used-car salesperson receives a commission of $ 200 plus 4 percent [#permalink]

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New post 15 Dec 2015, 16:14
Hi All,

This question can be solved by TESTing THE ANSWERS.

We're given the pay rate of two different salespeople who sell cars:
1) A commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price.
2) A straight commission of 6 percent of the car’s final sale price.

We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?

Let's TEST Answer B: $6,000

1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400
2nd salesperson = .06(6,000) = $360

These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...

Let's TEST Answer C: $8,000

1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480
2nd salesperson = .06(8,000) = $480

These totals are the SAME, so this must be the answer.

Final Answer:
[Reveal] Spoiler:
C


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Re: One used-car salesperson receives a commission of $ 200 plus 4 percent [#permalink]

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New post 15 Dec 2015, 22:03
Let the price be x

[4% = 1/25 and 6% = 3/50]
200 + (1/25)(x - 1000) = (3/50)x

Multiply throughout by 50

10000 + 2x - 2000 = 3x
x = 8000

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Re: One used-car salesperson receives a commission of $ 200 plus 4 percent [#permalink]

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New post 15 Dec 2015, 23:24
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

One used-car salesperson receives a commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?

A. $ 5,000
B. $ 6,000
C. $ 8,000
D. $ 10,000
E. $ 12,000



Let the final sale price be x. Then we have (x-1000)*(4/100) + 200 = x*(6/100). By multiplying 100 to both sides we have 4x-4000 + 20000=6x. So we get 16000=2x ---> x=8000

The answer is, therefore, (C).
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Re: One used-car salesperson receives a commission of $ 200 plus 4 percent [#permalink]

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New post 10 Apr 2016, 11:42
test for various answer options one by one
test for option A
200 +0.04*(5000 - 1000) is not equal to 0.06*5000
test for option B
200 +0.04*(6000 - 1000) is not equal to 0.06*6000
test for option C
200 +0.04*(8000 - 1000) is equal to 0.06*8000 = $480
therefore correct answer option C

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Re: One used-car salesperson receives a commission of $ 200 plus 4 percent [#permalink]

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New post 25 Oct 2017, 06:20
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Re: One used-car salesperson receives a commission of $ 200 plus 4 percent   [#permalink] 25 Oct 2017, 06:20
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